I'd tend to agree - we're not even remotely cautious about claims about the pace of climate change. For example, a few months ago there was a (now largely retracted) scientific paper claiming the oceans had been soaking up much more heat than previously thought due to global warming, something like 60% more:
https://news.ycombinator.com/item?id=18352506This was clearly suspect. The paper used a weird, indirect method to measure something that we could measure pretty much directly and got results that contradicted the direct measurements. The obvious conclusion was that their measurement method didn't work and it should've required some really strong evidence to overcome that presumption. Yet the entire press ran terrifying headlines and stories treating its conclusions as indisputable facts showing our world was even more doomed than previously though and the HN discussion was dominated by prophecies of doom.
It fell to a climate change skeptic to figure out that they'd substantially underestimated the margin of error in their calculations and that their complicated indirect measurement method simply wasn't accurate enough to conclude that the oceans had absorbed more heat than the previous measurements said. Which is why it's been corrected and the better news outlets have published corrections abandoning the original claims of doom which, naturally, most of the people who saw the original terrifying stories would never see.